Electric circuits and resistance

[phattestlewt]

This question's explanation is bugging me

TBR question

For two cylindrical resistors made of identical material and with equal radii, R1 and R2, where R1 is longer than R2, what is true when the two are in parallel?

A. R1 dissipates more heat than R2
B. R2 dissipates more heat than R1
C. R1 experiences a greater voltage drop than R2
D. R2 experiences a greater voltage drop than R1.

C/D eliminated because voltage drops are the same when in parallel.

R = rho*l/A

Areas cancel out because they have the same cross-sectional area. And based solely on the lenghts, R1 has a greater length and thus a greater resistance. Don't metals with greater resistance dissipate more heat?

Shouldn't the answer be A?

Why is it B though?
Or do I have it reverse. Metals with lower resistance dissipate more heat? Just a little confused here, any clarification would help.
Thanks ^^

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[pjk77]

So the key here is "in parallel"
The way I think of it is that the heat comes from the current that passes through the resistor.
So if the resistors were in series, and the current was the same, then the larger one would dissipate more heat just because its longer and has the greater surface area.
Since the resistors are in parallel, the smaller resistor carries more of the current, and thus dissipates more of the heat.

 

[broski123]

Remember that in parallel, voltage drop is equal, but current is different. More current will travel to the pathway with the least resistance.

 

[SpaceBuff12]

V = I1R1 = I2R2; P1 = (I1^2)*R1; P2 = (I2^2)*R2.

Since we know that the current through R2 is greater than the current through R1, R2 will dissipate I2/I1 times more heat.

 

[orangeblue]

Hello guys, another related Circuits question. TBR BK II Physics: pg 202.


statement 1 from passage: Under figure 2, it says "if two resistors experience same current, one will the greatest resistance will dissipate most heat"

In Figure 2 above, the 25 Ohm resister is gives a bigger temperature change than 100 ohm resister. I don't understand this b.c it says that each resister is connected to 12-Volts so V= IR. Since V is the same, the bigger resister has smaller I (current) and the smaller resistor has bigger current. Right?
This is why statement 1 doesn't apply in this case as current is different. MCAT does this kind of thing : puts a statement beneath an example but it doesn't really apply to figure?(it seems rare though)

In question 3, I don't understand why statement (IV): increasing the resistance of a resistor doesn't increase the rate of temperature increase?

 

[orangeblue]

Also, by heat dissipation : it really just means P (since P = energy/time hence it's a rate)?

 

[broski123]

Hello guys, another related Circuits question. TBR BK II Physics: pg 202.


statement 1 from passage: Under figure 2, it says "if two resistors experience same current, one will the greatest resistance will dissipate most heat"

In Figure 2 above, the 25 Ohm resister is gives a bigger temperature change than 100 ohm resister. I don't understand this b.c it says that each resister is connected to 12-Volts so V= IR. Since V is the same, the bigger resister has smaller I (current) and the smaller resistor has bigger current. Right?
This is why statement 1 doesn't apply in this case as current is different. MCAT does this kind of thing : puts a statement beneath an example but it doesn't really apply to figure?(it seems rare though)

In question 3, I don't understand why statement (IV): increasing the resistance of a resistor doesn't increase the rate of temperature increase?

I'm confused, you just contradicted yourself. The statement on the bottom says "same current", whereas you just said that lower the resistor, larger the current. Maybe you misread, but same voltage drop =/= same current. Power is current squared times resistance. Therefore current is more important in heat loss.

 

[orangeblue]

In parallel cases: V = IR so even if V is same, different resistor will have different current going through it.

The passage says "if two resistors experience same current, one will the greatest resistance will dissipate most heat" <---- this only applies for resistor in series, b.c that's the only time two resistors will have the same current going through it.
Correct?

 

[sps27]

In parallel cases: V = IR so even if V is same, different resistor will have different current going through it.

The passage says "if two resistors experience same current, one will the greatest resistance will dissipate most heat" <---- this only applies for resistor in series, b.c that's the only time two resistors will have the same current going through it.
Correct?

Yes, that is correct. The term I^2 * R * t explains it all. If resistors are in series the I^2 term is same for both. So the deciding factor is Resistance. Higher resistance will generate more heat etc., If resistors are in parallel, the smaller resistance has bigger current which varies by square, hence smaller resistance generates more heat.